Equilibration time in many-body quantum systems

Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from perturbation to equilibration, of a paradigmatic disordered many-body quantum system in the chaotic regime and as we approach the many-body localization transition. We investigate how the equilibration time depends on the system size and observables. We show that if dynamical manifestations of spectral correlations in the form of the correlation hole ("ramp") are taken into account, the time for equilibration scales exponentially with system size, while if they are neglected, the scaling is better described by a power law with system size, although with an exponent larger than what is expected for diffusive transport.